Direct Top Quark Decay Width Measurement in the tt Lepton+Jets Channel at 8 TeV with the ATLAS Experiment

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Direct Top Quark Decay Width Measurement in the t ¯ t Lepton + Jets Channel at p

s = 8 TeV with the ATLAS Experiment

Dissertation

zur Erlangung des mathematisch-naturwissenschaftlichen Doktorgrades

„Doctor rerum naturalium“

der Georg-August-Universität Göttingen

im Promotionsprogramm ProPhys

der Georg-August University School of Science (GAUSS)

vorgelegt von

Philipp Stolte-Cord to Krax aus Göttingen

Göttingen, 2017

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II. Physikalisches Institut, Georg-August-Universität Göttingen Prof. Dr. Ariane Frey

II. Physikalisches Institut, Georg-August-Universität Göttingen Prof. Dr. Kevin Kröninger

Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund

Mitglieder der Prüfungskommission:

Referent: Prof. Dr. Arnulf Quadt

II. Physikalisches Institut, Georg-August-Universität Göttingen Koreferent: Prof. Dr. Stan Lai

II. Physikalisches Institut, Georg-August-Universität Göttingen

Weitere Mitglieder der Prüfungskommission:

Prof. Dr. Ariane Frey

II. Physikalisches Institut, Georg-August-Universität Göttingen Prof. Dr. Wolfram Kollatschny

Institut für Astrophysik, Georg-August-Universität Göttingen

Prof. Dr. Ulrich Parlitz

Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen

Prof. Dr. Steffen Schumann

II. Physikalisches Institut, Georg-August-Universität Göttingen

Tag der mündlichen Prüfung: 24.10.2017

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Direct Top Quark Decay Width Measurement in the t ¯ t Lepton + Jets Channel at p

s = 8 TeV with the ATLAS Experiment

Philipp Stolte-Cord to Krax

Abstract

The top quarktplays an essential role in the field of elementary particle physics - in particular due to its exceptional properties comprising a large mass, which approximately equals the mass of a tungsten atom, and an enormously short lifetime. This thesis is devoted to the study of a fundamental property of the top quark - its decay width. Its value is predicted by the established Standard Model of particle physics and deviations may hint at yet unknown physics beyond this model.

A direct measurement of the decay width of the top quark is presented. The analysis is based ont¯tevents in the lepton+jets decay channel using data taken in proton-proton collisions at a centre-of-mass energy of ps=8 TeV. The dataset was recorded in 2012 with the ATLAS detector at the Large Hadron Collider at CERN and corresponds to an integrated luminosity of 20.2 fb⁻¹. The decay width of the top quark is extracted by utilising a template fit to one-dimensional distributions of kinematic quantities, performed simultaneously in the hadronic and the leptonic decay branch oft¯tevents. Since the measurement is a direct measurement of the top quark decay width, it is less model-dependent in comparison to indirect approaches. This enables the measurement to probe a broad class of Standard Model extensions.

II.Physik-UniGö-Diss-2017/03 II. Physikalisches Institut

Georg-August-Universität Göttingen

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Direkte Zerfallsbreitenmessung des Top-Quarks im t ¯ t -Lepton + Jets-Zerfallskanal bei p

s = 8 TeV mit dem ATLAS-Experiment

Philipp Stolte-Cord to Krax

Zusammenfassung

Das Top-Quark tspielt eine wesentliche Rolle im Bereich der Elementarteilchenphysik - insbesondere auf- grund seiner bemerkenswerten Eigenschaften, die eine sehr große Masse, die in etwa mit der eines Wolfram- atoms vergleichbar ist, sowie eine enorm kurze Lebensdauer umfassen. Ziel dieser Arbeit ist die Untersuchung einer fundamentalen Größe des Top-Quarks - der Zerfallsbreite. Der Wert der Zerfallsbreite wird vom eta- blierten Standardmodell der Teilchenphysik vorhergesagt, und Abweichungen können auf Physik jenseits dieses Modells hinweisen.

Diese Dissertation stellt eine direkte Messung der Zerfallsbreite des Top-Quarks vor. Die Analyse basiert auf t¯t-Ereignissen im Lepton+Jets Zerfallskanal und nutzt Analysedaten, die in Proton-Proton-Kollisionen bei einer Schwerpunktsenergie vonp

s=8 TeV genommen wurden. Der Datensatz wurde im Jahr 2012 mit dem ATLAS-Detektor am Large Hadron Collider am CERN aufgezeichnet und entspricht einer integrierten Lumino- sität von 20.2 fb⁻¹. Die Zerfallsbreite des Top-Quarks ergibt sich mittels eines sogenannten Template-Fits an eindimensionale Verteilungen verschiedener kinematischer Größen. Jener Fit ist simultan im hadronischen und leptonischen Zerfallszweig dert¯t-Ereignisse realisiert. Da die Messung auf direkte Weise durchgeführt wird, ist sie modellunabhängiger als indirekte Methoden, was die Prüfung einer breiten Klasse von Standard- modellerweiterungen erlaubt.

II.Physik-UniGö-Diss-2017/03 II. Physikalisches Institut

Georg-August-Universität Göttingen

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1 Introduction

One of the most fundamental questions which has bothered scientists for generations is concerned with the basic orelementaryconstituents of matter, examined at the smallest possible scale. Con- sequently, these constituents are referred to as particles or elementary particles. But what does elementary or, generally speaking,elementary particle physicsmean?

The underlying definition of the term “elementary” has evolved significantly over time - although the aim of this field of physics is still the same: the hunt for those fundamental constituents and their possible interactions, which gained pace remarkably over the last decades. Chemists in the 19th century can perhaps be regarded as the first researchers in the field of particle physics since they discovered distinct elements postulated to be composed of atoms, whose name originates fromátomos, the Greek word for “uncuttable”. These discoveries resulted in the periodic table of chemical elements, first published by the Russian chemist D. Mendeleev in 1869. The discovery of the electron by J. J. Thomson in 1897 marks the starting point of subatomic particle physics followed by the gold foil experiments, the first fixed target experiments, performed by H. Geiger, E. Marsden and E. Rutherford between 1908 and 1913, leading to Rutherford’s proposal of a model where the atom is mostly empty, and the positive charge inside atoms is concentrated in a point-like and massive centre, the atomic nucleus, which is surrounded by a cloud of electrons.

Due to technological improvements in the 1950s and later decades allowing for the development of more advanced particle accelerators and detectors, more and more subatomic particles could be discovered; in addition to the positively charged proton and the electrically neutral neutron, being the constituents of the atomic nuclei. Many of these newly discovered particles were included in the “eightfold way”, introduced by M. Gell-Mann. Later, based on deep-inelastic scattering, it was experimentally verified that also protons and neutrons are not elementary but compound particles composed of quarks. Further developments and in particular the electroweak theory by S. Glashow resulted in the formulation of the Standard Model of Elementary Particle Physics which describes all elementary particles and their interactions while the particle masses are explained by the Higgs mechanism. Today’s experiments in the field of particle physics, around 120 years after the discovery of the electron, are based on collisions of particles obtaining their high energy from accelerators which is why the expressionhigh energy physicsis commonly used to characterise those experiments. After the acceleration and collision of particles, the resulting decay products need to be measured with precise particle detectors to draw inferences about the underlying processes and the involved particles, which comprises, for example, a measurement of their properties.

Caused by a decreasing distance scale of the observed processes, higher energies and, as a result, larger machines are essential to accelerate particles before colliding. Nowadays, theLarge Hadron

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Collider (LHC) at CERN, the European Organisation for Nuclear Research, is the world’s most powerful particle accelerator which started operating with beam energies of 3.5 TeV in 2010, and is designed to reach beam energies of up to 7 TeV. These high energies, in combination with a high luminosity, which can be described as the number of occurring events per time and area, allowed for the discovery of a new boson at the LHC. The observation was announced in July 2012[1, 2], observed by the two LHC multipurpose experiments ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid). Further measurements in the past years confirmed that this new particle is indeed the Standard Model Higgs boson, which has been searched for since its prediction in the 1960s [3–13]. Additionally, this high energy regime enables particle physicists to test the Standard Model in more detail, and it may unveil something unsuspected, commonly classified as physics beyond the Standard Model.

The Standard Model fermion with the strongest coupling to the Higgs boson is the top quark due to its relatively large mass, which is of the order of the tungsten atom mass. Hence, the lifetime of the top quark is expected to be rather small and, consequently, the decay width of this heaviest quark very large. Measuring the top quark decay width is of strong interest since deviations from the Standard Model decay width expectation would be an indication of new and yet unknown physics.

For example, such deviations may hint at currently unknown top quark decay channels - such as decays through a charged and yet undetected Higgs boson, decays through the supersymmetric partner of the top quark or a flavour changing neutral current decay of the top quark.

This thesis intends to present a direct measurement of the top quark decay width. The most con- spicuous characteristic of such a direct measurement is its model-independence as fewer Standard Model assumptions need to be made - in comparison to an indirect measurement, which is defined in the following chapters. Thus, a direct measurement serves to probe a potentially broader class of models involving Standard Model extensions.

The most recent direct measurements of the top quark decay width were performed at the Tevatron by the CDF collaboration[14]and at the LHC by the CMS collaboration[15]. The CDF measurement is based on the Tevatron dataset ofp

s =1.96 TeV proton-antiproton collision data which corresponds to an integrated luminosity of 8.7 fb⁻¹. A decay width of 1.10<Γt <4.05 GeV for a top quark mass of 172.5 GeV was extracted at the 68% confidence level. The preliminary CMS result was obtained using 12.9 fb⁻¹of proton-proton collision data taken at the LHC in 2015 and 2016 at a centre-of-mass energy ofp

s= 13 TeV yielding a range of 0.6<Γ_t < 2.5 GeV for the decay width at the 95% confidence level.

Performing a direct measurement is very challenging because of the limited detector resolution for objects used to define observables needed to extract the top quark decay width. This resolution, provided by large multipurpose detectors like ATLAS and CMS, translates into smeared and broad- ened observable distributions with resolutions which are around one order of magnitude larger than the expected underlying decay width itself. As a result, extensive optimisation studies need to be carried out to find a well-suited and sophisticated analysis setup to extract the decay width

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out of the given dataset and ease the effort of such a demanding measurement, which was one of the most relevant aspects of the analysis presented in this thesis.

The measurement is based on data which was recorded with the ATLAS detector at a centre-of-mass energy ofp

s=8 TeV at the LHC in 2012 using proton-proton collision data. It is performed in the lepton+jets decay channel oft¯t events with one of the two top quarks decaying into a bquark and aW boson that decays further into two quarks, denoted as the hadronic decay branch, while the other top quark decays into a bquark and aW boson decaying further into a charged lepton, namely an electron or a muon, and the corresponding neutrino, representing the leptonic decay branch.

The decay width is determined using a template method. The required templates are generated with Monte Carlo simulations for signal and all background contributions except for multijet processes with misidentified leptons for which a data-driven method is exploited. In order to generate signal templates for different values of the top quark decay width, a reweighting method is applied. These templates enter a binned likelihood fit to data to measure the decay width. The fit is performed using templates of two different observables sensitive to the top quark decay width simultaneously.

One observable is defined using the hadronically decaying top quark whereas the other depends on the leptonically decaying top quark kinematics to take advantage of the full information of t¯t events. The latter observable is the reconstructed invariant mass of the system formed by the bjet and the charged lepton`from the leptonic top quark decay,m_`b. The other observable is the angular distance between the bjet j_bassociated with the hadronic top quark and the closest light jet j_l from the hadronically decayingWboson,∆Rmin(j_b,j_l). These observables and the underlying quantities and angles are defined in detail in the upcoming chapters.

The input distributions used in the fit are split into two pseudorapidity regions to isolate a region which suffers less from detector resolution and pile-up effects. Pile-up effects refer to the effect of multiple ppinteractions from the same or previous bunch crossings in the detector. The events are also split according to the charged lepton flavour (electron or muon) and, finally, split into events where exactly one or at least two jets are tagged as originating from abquark. Thus, concatenated distributions composed of eight individual channels constitute the templates utilised in the binned likelihood fit. The fit and the entire analysis strategy are explained in the following chapters in more detail.

Before the main topic of this thesis can be thoroughly discussed, more fundamental aspects need to be delineated first. Chapter 2 contains an introduction into the Standard Model of Particle Physics followed by the presentation of some detailed information about top quarks and their properties with a particular focus on the decay width of the top quark. The LHC and the ATLAS detector including the most significant features of its subsystems are depicted in Chapter 3.

Chapter 4 serves to outline the reconstruction of physics objects used in the analysis whereas the dataset and the Monte Carlo generators employed to simulate signal and all background events are introduced in Chapter 5. In Chapter 6, fundamentals of the event selection and reconstruction, also covering studies on the agreement between data and prediction, are described. Special emphasis is

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placed on different options and extensions of the tool used to reconstructt¯tsignal events. Chapter 7 gives a detailed description of the likelihood fit and the underlying machinery. This includes the definition of the observables sensitive to the top quark decay width, the template reweighting, the fit method validation and studies of fit configurations. Chapter 8 is devoted to the definition and evaluation of systematic uncertainties including studies which aimed at reducing dominant systematic uncertainties affecting the measurement. A dedicated observable comparison based on leading systematic effects is delineated in Chapter 9. The subsequent Chapter 10 contains the results of the analysis. Eventually, a summary of the performed measurement and a brief outlook are presented in Chapter 11.

Feynman diagrams used to illustrate various processes, especially in the following chapter, are drawn with thetikzfeynmanpackage[16].

The following unit systems are used throughout the thesis: The familiar SI unit system with metres, kilograms and seconds is mainly employed in Chapter 3 to express various dimensions of the detector. Most other sections bear on the use of natural units according toħh=c =1, withħhas the reduced Planck constant and c as the speed of light. This implies that energies, masses and momenta are usually written in the unit of electron volt, eV, while time and length are given as 1/eV. Thus, also decay widths, which correspond to the inverse of the decay time in natural units, are expressed in units of eV.

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2 The Standard Model and the Role of the Top Quark Therein

The Standard Model of Particle Physics, usually denoted as the Standard Model or abbreviated as SM, involves the top quark and predicts properties of this quark as they are presented in the context of this thesis. Hence, the fundamental principles and the theoretical framework of this model are outlined in the first part of this chapter. The top quark production channels, decay modes as well as properties of this quark are discussed in detail in the second part. Special emphasis is placed on the decay width of the top quark Γt as a direct measurement of this quantity is presented in this thesis. The corresponding sections also cover recent measurements ofΓtas well as physics models beyond the SM (BSM) which predict deviations from the decay width value calculated within the Standard Model.

2.1 The Standard Model of Particle Physics

The Standard Model emerged from the 1960s and 1970s and characterises all known elementary particle interactions excluding gravity. Nowadays, no other theoretical framework allows for a more precise description of elementary particles, their interactions and properties which are measured to a high accuracy in a variety of experiments. The SM serves to describe two types of elementary particles, namely fermions (comprising the so-called quarks and leptons) and bosons including the so-called mediators or force carriers, referred to as gauge bosons. The following theories are incorporated in the SM: quantum electrodynamics (QED), the Glashow-Weinberg-Salam theory of electroweak (EW) processes[17–19]and quantum chromodynamics (QCD)[20–22].

All the different interactions between the initially massless quarks and leptons, whose masses are generated by the so-called Higgs mechanism[23, 24]complying with the laws of EW theory, are mediated by the gauge bosons. The relationship between this mechanism and another massive scalar elementary particle included in the SM, which is correspondingly called Higgs boson, is part of Sec. 2.1.2. Quantum mechanics and special relativity are incorporated into a quantum field theory based on the concept of gauge symmetry in order to describe the interactions between the SM particles. In this connection, the generalised formalism of Lagrangian mechanics is adapted to SM fields and particles, mathematically expressed by operators that are subject to a certain space-time point, while the Lagrangian density is a function of these fields and their space-time derivatives.

As the SM rests on a combination of local gauge symmetries, it gives rise to conservation laws in compliance with Noether’s theorem. These SM concepts are delineated in the following sections.

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2.1.1 Quarks, Leptons and Mediators

Three kinds of elementary particles are differentiated by the Standard Model, as introduced in the last paragraph: leptons,quarksandbosons. The first two categories constitute spin-1/2-particles, thefermions, while the SM bosons, which carry integer spin, include the Higgs boson and gauge bosons, the latter also referred to asmediators.

Quarks and leptons are grouped into threegenerationshaving increasing masses. Each generation is composed of two out of the six existing lepton or quark “flavours”, respectively. This scheme also describes antifermions with opposite quantum numbers, such as electric charge, but same mass as the corresponding fermion - on the assumption ofCPT(charge parity time) conservation. The definition of leptons is based on the quantities: chargeQ, electron numberL_e, muon numberL_µand tau number L_τ. The six quark flavours are specified by charge, upnessU, downnessD, strangeness S, charmnessC, bottomnessB and topnessT, related to the name of the quarks[25, 26].

All quarks and leptons form left-handeddoubletsbut right-handedsinglets, deduced by taking the concepts of chirality and handedness into account, resulting in three generations of left-handed leptons arranged as:

ν_e e

L

,

ν_µ µ

L

,

ν_τ τ

L

.

Hence, the lepton generations consist of an electrically neutral neutrinoνiand a negatively charged lepton`=e,µ,τwithQ=−e. The left-handed up-type quarks (u, c, t) with chargeQ=2/3·e and the left-handed down-type quarks (d,s, b) with negative chargeQ=−1/3·eare written as:

u d⁰

L

,

c s⁰

L

,

t b⁰

L

.

The (d⁰,s⁰,b⁰) cited in the left-handed doublets constitute the weak eigenstates being different from the mass eigenstates which represent the quarks d,sandb. As these weak eigenstates are linear combinations of the mass eigenstates, the mixing of the three quark generations can be described by a 3×3 matrix, the Cabibbo-Kobayashi-Maskawa (CKM) matrix, denoted asV [27]:





 d⁰

s⁰ b⁰





=V·





 d s b





=







V_ud V_us V_ub V_cd V_cs V_{c b} V_{t d} V_ts V_{t b}





·





 d s b





.

Given the unitarity of V, four parameters are sufficient to characterise this matrix, three real parameters, the mixing angles, and one imaginary phase factor, responsible for C P(charge parity) violation[28, 29]. Analogously, the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix[30, 31] is formulated for the lepton sector serving to mathematically describe neutrino oscillations.

The SM particles and their properties are listed in Table 2.1 [25, 28]. The weak hypercharge Y, defined asY =2(Q−T₃), is also given. The values of the third component of the weak isospinT₃

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2 . 1 T H E S TA N D A R D M O D E L O F PA RT I C L E P H Y S I C S

explain the order of fermions in the doublets shown above.

Particles Q[e] C s T₃ Y

Leptons

νe

e

L

ν_µ µ

L

ν_τ τ

L

0

−1

- ¹₂

+¹₂

−¹₂

−1

e_R µR τR −1 - ¹₂ 0 −2

Quarks

u d⁰

L

c s⁰

L

t b⁰

L

+²₃

−¹₃

r,g,b ¹₂

+¹₂

−¹₂

+¹₃

u_R c_R t_R +²₃ r,g,b ¹₂ 0 +⁴₃

d_R s_R b_R −¹₃ r,g,b ¹₂ 0 −²₃

Gauge Photonγ 0 - 1 0 0

bosons Z⁰ 0 - 1 0 0

W^± ±1 - 1 ±1 0

8 Gluons g 0 r,g,b 1 0 0

Higgs boson 0 - 0 −¹2 +1

Table 2.1: Particles and mediators in the Standard Model. Given are the particle properties electric chargeQ, colourC, spins, the third componentT₃of the weak isospinT as well as weak hyperchargeY [25, 28].

The quarks and their antiparticles, except for top quarks, as discussed in Chapter 2.2.3, formhadrons which are categorised intomesonscarrying integer spin andbaryonswith an odd half-integral spin.

Confinement, introduced in Section 2.1.2, causing the coupling strength to increase with distance, explains why quarks cannot act as free particles. Furthermore, quarks denote the only elementary particles that are able to interact via all fundamental forces of the Standard Model[25, 26]. The fermions cover a broad range of masses, shown in Table 2.2. The top quark mass is by far the largest, hinting at a possible special role in the framework of the Standard Model, which will be described more thoroughly in Section 2.2.

Lepton Massmin[MeV] Quark Massmin[MeV] e[32] 0.5109989461(31) u[38, 39] 2.2⁺₋^0.6_0.4 µ[33] 105.6583745(24) c[40, 41] 1280± 30 τ[34] 1776.86(12) t [42, 43] 173100±600 ν_e [35] <2·10⁻⁶ d [38, 39] 4.7⁺₋^0.5_0.4 ν_µ [36] <0.19 s[38, 39] 96⁺⁸₋₄

ν_τ[37] <18.2 b[44] 4180⁺⁴⁰₋₃₀

Table 2.2:Masses of fermions according to [28]. More information concerning the top quark mass is given in Section 2.2.3. The values given for the neutrinos are not mass eigenstates. The listed references cite the discovery of the corresponding particle.

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2.1.2 Interactions and the Higgs Mechanism

The mathematical foundations of the Standard Model regarding the three elementary particle interactions contained in the model, i.e. electromagnetic, weak and strong ones, is outlined in this subsection. Since the SM is a gauge theory, these interactions are characterised by local gauge symmetries implying that the Lagrangian is locally invariant under a transformation of a specific gauge group, denoted asLie group. Two types of Lie groups are relevant for a description of the SM: unitary and special unitary Lie groups, abbreviated asU andSU. The number of generators of a group from the mathematical point of view conforms with the number of gauge fields associated with a certain interaction and amounts to n² (in case of aU(n)group) or n²−1 (SU(n) group).

The value ofn²−1 is consistent with the dimension of a group with ordern.

Electroweak Theory

As the name indicates, the electroweak theory comprises a description of electromagnetic and weak processes. The former interactions are characterised by the unitary Abelian Lie groupU(1)emwith the phase transformationφ →φ⁰=eⁱ^θφ with a spinor fieldφ and a real numberθ ∈R. Weak interactions, on the contrary, are described by aSU(2)group which is generated by the threePauli matricesσi withi=1, 2, 3. The underlying phase transformation for this interaction with the Pauli matrices isφ→φ⁰=eⁱ^~σ·~αφwith~α= (α1,α2,α3)whereα1,α2,α3∈R. These two interactions are both combined to the symmetry groupSU(2)_L⊗U(1)_Y by the electroweak theory, introduced by S. Glashow, A. Salam and S. Weinberg in the 1960s[17–19], due to their surnames also abbreviated as GSW or GWS theory. The above given indices are chosen because Limplies that the weak isospin current couples only to left-handed fermions whileY represents the weak hypercharge, which is the generator of the groupU(1)Y, including the electromagnetic processes.

The following massless gauge fields are associated withSU(2)L⊗U(1)Y: a single vector fieldB_µ (forU(1)Y) which couples to the weak hypercharge current j_µ^Y with a strength commonly denoted as ^g₂⁰ and an isotriplet of vector fieldsW_µⁱ (forSU(2)L, indicesi=1, 2, 3 as above) with a coupling strength gand a weak isospin currentJ_µⁱ. This results in the following expression for the basic EW interaction:

−i·g(Jⁱ)^µW_µⁱ−i· g⁰

2(j^Y)^µB_µ.

The mixing between the two groupsSU(2)L andU(1)Y is described by an angle denoted as the Weinberg angle orweak mixing angleθ_W. The relationship between this angle and the coupling strengths can be expressed by either:

sinθ_W = g⁰

pg²+g⁰² and tanθ_W = g⁰ g .

The measured value amounts to sin²θW =0.23129±0.00005[28]and relates the electromagnetic charge with the given coupling constantsgandg⁰: e=g·sinθW =g⁰·cosθW. Linear combinations

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of the gauge fields lead to equations for the associated gauge bosons. Using the neutral fieldsW_µ³ andB_µ, the following definitions for the neutral gauge bosons,γandZ⁰, as the mediators of the neutral currents of electromagnetism and weak interactions, respectively, can be obtained using a matrix containing solely the mixing angles:

A_µ Z_µ

=

cosθ_W sinθ_W

−sinθW cosθW

B_µ W_µ³

,

which leads to the two separate equations:

A_µ= B_µcosθW +W_µ³sinθW (bosonγ), Z_µ=−B_µsinθW +W_µ³cosθW (bosonZ⁰).

The two remaining fieldsW_µ¹ andW_µ² are used to define the two charged bosons as:

W_µ^±= v t1

2(W_µ¹∓i·W_µ²) (charged bosonsW^±). The full Lagrangian of the electroweak theory has the following form:

LEW=−1

4W_µνⁱ W_i^µν−1

4B_µνB^µν +Lγ^µ(i∂_µ−gσ_i

2W_µⁱ− g⁰

2Y B_µ)L+Rγ^µ(i∂_µ− g⁰

2Y B_µ)R.

The interactions between the gauge fields themselves are described by the first two terms, the two remaining terms characterise the interactions between the particles that are mediated by the corresponding gauge bosons. According to their abbreviation, LandRas wave functions signify a left-handed fermion doublet and a right-handed fermion singlet of fermion spinors.

The vertex for the weak interaction has a vector-axial vector (V-A) structure which mathematically expresses the parity violation of the weak interaction.

All four gauge bosons described by the electroweak theory are obtained from linear combinations of massless gauge fields. Hence, the gauge bosons are massless in this model which is in contradiction to experiments which have proven the massiveness of the three bosonsW^±andZ⁰(commonly the simpler notationW andZ is used). These massive gauge bosons indicate the symmetry breaking of theSU(2)L⊗U(1)Y group, and thus the electroweak model needs to be extended.

Higgs Mechanism

This extension is realised by the Higgs mechanism with the so-called Higgs boson. This mechanism explains how particle masses are generated in a gauge invariant way[23, 24].

A first naive approach based on adding explicit mass terms for the massive gauge bosonsW andZ to the Lagrangian would violate gauge invariance and lead to unrenormalisable divergences. The massive gauge boson masses, however, can be incorporated by spontaneous symmetry breaking

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of the vacuum ground state which keeps the Lagrangian gauge invariant. For this purpose, four real scalar fieldsφ_kare defined which are elements ofSU(2)⊗U(1)and integrated into an isospin doublet with weak hyperchargeY =1 as follows:

φ=

φ⁺ φ⁰

with φ⁺= (φ1+iφ2)/p 2 , φ⁰= (φ3+iφ4)/p

2 .

A coupling of this complex scalar doublet to the gauge bosons, which is responsible for the symmetry breaking as shown later, results in an additional gauge invariant Lagrangian:

LHiggs= (D_µφ)^†(D^µφ)−V(φ^†φ),

with a covariant derivative D_µ. The term V(φ^†φ) constitutes the most general renormalisable potential, the Higgs potential, depending only on the combinationφ^†φand defined by the choice of the parametersµandλ:

V(φ^†φ) =µ²φ^†φ+λ(φ^†φ)².

The parameter v represents the vacuum expectation value and is, in case ofµ² < 0 andλ > 0, given by v² = −µ²/λ. The choice of the ground state φ0(v), depending on v, is arbitrary. An appropriate option withφ1=φ2=φ4=0 andφ3=v yields:

φ0(v) = 1 p2

0 v

, (2.1)

which is invariant with respect to the underlying U(1)em symmetry. For the scalar Higgs SU(2) doublet, an expansion around the ground state yields:

φ(x) = 1 p2

0 v+H(x)

.

The SU(2)L⊗U(1)Y symmetry is spontaneously broken by using the vacuum state defined in Eq. (2.1) if v6=0. As theU(1)em symmetry is still kept, the photon remains massless as desired.

This spontaneous symmetry breaking gives rise to the creation of a real massive boson, identified with the Higgs boson, having spin 0 and a mass ofm²_H=2v²λ. Based on the mathematical terms and assumptions shown above, the final Lagrangian of the Higgs fields contains, apart from a kinetic part, mass terms for the bosons including the Higgs, terms for trilinear (HW⁺W⁻ andH Z Z) and quartic (H HW⁺W⁻ andH H Z Z) couplings, as well as terms for the Higgs self-coupling.

The masses which the gauge bosons acquired by the Higgs mechanism are:

m_W = 1

2v g and m_Z= 1 2vÆ

g²+g⁰²,

in terms of the vacuum expectation value v. The photon mass is zero, m_γ = 0, as described

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above. The vacuum expectation value is related to the Fermi coupling constant G_F via v = 1/Æp

2G_F ≈246.2 GeV. The current world average of the Higgs boson mass amounts to m_H = 125.09±0.21(stat.)±0.11(syst.)GeV[28]. The value of the Higgs mass is not predicted by this theory before due to the fact that the parametersµandλwere unknown.

The Higgs mechanism also generates the masses of fermions whose couplings to the Higgs field are described by the Yukawa coupling y_f. The mathematical expression is obtained after adding the required corresponding term to the Standard Model Lagrangian, resulting in the relationship:

m_f = 1 p2v y_f ,

indicating a direct proportionality between fermion mass and Yukawa coupling sincevis a constant.

Hence, the top quark as the fermion with the highest mass, see Table 2.2, has the largest coupling to the Higgs field compared to all other fermions: y_t≈1.

Quantum Chromodynamics

The third interaction, the strong one, is described by quantum chromodynamics using the non- Abelian symmetry groupSU(3)C. The matricesT_a=λa/2 based on the eightGell-Mann matricesλa, witha=1, 2, ..., 8, serve as generators of this group. The phase transformation isq→q⁰=eⁱ^αâ^Tâq with the group parametersαa and the quark fieldq. Eight gluon fieldsG_µâ for the eight massless gluons as mediators of the strong interaction need to be distinguished. They carry colour charge themselves, the quantum number of the strong interaction, which is labelled asC, being the index of the group definition. The colour states red, blue and green with corresponding anticolours exist. Merely colourless bound states are invariant underSU(3)C transformations. The full QCD Lagrangian containing the gluon fields, the massmfor a quark, the coupling constantg_s=p

4παs

and the quark field can be written in the following form:

LQCD=¯q(iγ^µ∂_µ−m)q−g_s¯qγ^µT_aqG_µ^a−1

4G_µν^a G_a^µν.

The givenG_µν^a constitute field strength tensors including a term for the self-interaction between the gauge bosons as carriers of the colour charge:

G_µνâ =∂_µG_νâ−∂_νG_µâ−g_sf_{a bc}G_µ^bG_ν^c,

with the structure constantf_{a bc}providing a relationship between the generator matrices:[T_a,T_b] = i f_{a bc}T_c.

In contrast to all other fundamental forces, the strong force increases with distance and decreases with smaller scales and higher energies, respectively. Thus,αsas a measure of the coupling strength cannot be regarded as a constant. It depends on the energy scale of the physical process, as additional internal loops affect its value. Consequently, to take these higher order corrections into account,αs is defined at a certain energy scale, arenormalisation scaleµR, resulting in an effective

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coupling. The following relationship betweenαs and an energy scaleQ² using the renormalisation scaleµ²_R holds:

α_s(Q²,µ²_R) = αs(µ²_R)

1+α_s(µ²_R)¹¹ⁿ₁₂^C⁻_π²ⁿ^f ln(^Q_µ²2 R

).

The parametern_f defines the number of active quark flavours f andn_C the number of coloursC. This formula describes the behaviour of the strong interaction at small and large scales, as depicted above.

For smaller energiesQ²→0 which corresponds to increasing distances,αs increases as well. Due to this effect, called quark confinement, free quarks, i.e. those outside of bound states, are not observed in nature. As a result, the creation of a quark pair having opposite colour charge is energetically preferred at high energies, in contrast to a separation of quarks. Thus, new bound states arise containing the original two quarks. Quark confinement is therefore the explanation for the formation of jets of hadrons diverging from the collision point when quarks are produced in such high energy collisions. As already mentioned, top quarks play a special role and cannot be observed in bound states, which is delineated in more detail in the next subsection.

On the other hand, for larger energiesQ²→ ∞, i.e. smaller distances close to zero,αs decreases and reaches zero asymptotically. Consequently, quarks in these extreme cases can be regarded as free quarks which is why QCD in the Standard Model is described asasymptotically free[25, 45].

Summary of Standard Model Interactions

In summary, the electroweak as well as the strong interactions can be joined together to form the Standard Model Symmetry Group:

SU(3)_C⊗SU(2)_L⊗U(1)_Y.

The different mediators of these interactions and their properties with additional information about the type of interaction are summarised in Table 2.3.

The Standard Model incorporates in total 18 different parameters whose values cannot be predicted by theory but have to be measured by experiments: the six masses of the quarks and the three masses of the charged leptons, the three mixing angles and the complex phase of the CKM matrix, the three couplings for the three SM gauge groupsU(1)Y,SU(2)L andSU(3)C, the Higgs boson mass and the vacuum expectation value v.

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Force Strong Electromagnetic Weak

Theory Chromodynamics Electrodynamics Flavourdynamics Mediator Gluon[46, 47] Photon[48, 49] W,Z[50–53]

Electric charge[e] 0 0 Q_W =±1

Q_Z=0

Colour 8 combinations - -

Coupling constant α_s(m_Z)≈0.1181 αem≈0.0073 α_w≈0.0316

Mass[GeV] 0 0 m_W =80.385±0.015

of mediators m_Z =91.1876±0.0021

Table 2.3:The three fundamental forces incorporated in the Standard Model and their properties [25, 28]. The variablesQ_W andQ_Z refer to the electric charge andm_W andm_Zto the masses of the massive bosons. The coupling constantsαi and g_i for the forces iare related to each other [45]. The given references cite the discovery of the corresponding particle.

All these predictions of the Standard Model have been tested to a very good level of accuracy over the last years, and the SM could meet every experimental observation in the past decades making it to one of the most successful theories in history. Nevertheless, despite the successful validation so far, the SM cannot be regarded as a complete theory, and a number of shortcomings need to be understood.

Gravity as the fourth fundamental force is not included in the SM and is solely described by the theory of general relativity developed by A. Einstein. The SM does not consider non-zero neutrino masses whereas these masses are implied by the existence of neutrino flavour oscillations[54–56]. Furthermore, the SM does not contain dark matter or dark energy, which form around 95% of the mass of the entire universe. In other words, merely 5% of the known amount of mass are made of matter described by the Standard Model.

Apart from that, the relatively large amount of free SM parameters listed above may hint at the existence of a more fundamental theory which contains the SM as an effective low-energy approx- imation. The SM is furthermore not able to explain the baryon-antibaryon asymmetry, i.e. the imbalance between the baryonic and the antibaryonic matter observable in our universe.

In the past years, various theories emerged which aim at resolving these problems of the Standard Model, predicting new particles or new types of interactions. Those theories involve supersymmetry, further dimensions or, for example, technicolor models. Some of these theories provide predictions for the effect on SM parameters and values like the top quark decay width, which is further discussed in Ch 2.3.3.

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2.2 The Top Quark

The existence of the top quark was proposed more than two decades before its experimental discovery. In order to explain the observation of CP violation[57]in 1964, Kobayashi and Maskawa proposed a third quark generation[27]which resulted in their formulation of a three-dimensional quark mixing matrix, the CKM matrix, as introduced in Sec. 2.1.1, in 1973. Four years later, the existence of the bquark as the first third generation quark was experimentally confirmed by the E288 experiment at Fermilab[44]with the discovery of theΥ meson, a meson which is composed of a band a ¯bquark. Hence, a weak isospin partner of the bottom quark to form the third quark generation was required and an almost two-decade period of searches began to find this quark, the so-called top quark. The search finally succeeded at the Tevatron collider in 1995. Since the top quark is not only the heaviest quark but even the heaviest SM particle (m_t>m_H >m_Z >m_W), the top quark could only be observed with the high collision energies reached at the Tevatron.

The top quark was discovered in t¯t production by both the CDF and DØ experiment at Teva- tron Run I, which operated at a centre-of-mass energy of p

s=1.8 TeV at the time using proton- antiprotonp¯pcollisions[42, 43]. Another 14 years later, the observation of electroweak production of single top quarks was confirmed by the CDF and DØ collaborations based on data taken at the Tevatron in Run II atp

s=1.96 TeV[58, 59]. The start of the LHC in 2008 marked the beginning of a new era of experimental top quark physics as top quarks are produced abundantly at the high centre-of-mass energies of the LHC. During Run I of the LHC, which includes the data-taking periods atp

s=7 TeV andp

s=8 TeV, more than ten million top quark events were produced at the two multipurpose detectors of the LHC, ATLAS and CMS, together. Such large amounts of data allowed for the realisation of many precision measurements in the field of top quark physics and the improvement of the Tevatron results. Efforts for measuring top quark properties in more detail are still very important since the heaviest quark, due to its large mass, is expected to play a distinct role in electroweak symmetry breaking mechanisms, as described in Sec. 2.1.2, and to provide a sign of new physics beyond the SM.

Before the top quark properties are presented in more detail, production mechanisms and decay modes of the top quark are described in the next subsections. Theoretical concepts like the QCD factorisation theorem or parton distribution functions are discussed as well. The chapter concludes with a section about the top quark decay width, the property of the top quark which is measured in the context of this thesis. Emphasis is placed on theoretical aspects of the decay width, recently published top quark decay width measurements and BSM theories which predict decay width values that differ from Standard Model expectations.

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2 . 2 T H E T O P Q U A R K

2.2.1 Top Quark Production

Two production mechanisms of top quarks exist at hadron colliders like the Tevatron and the LHC: electroweak production of single top quarks or top quark pair (t¯t) production via the strong interaction - whereby the latter process occurs much more frequently. Electroweak production of t¯t pairs is negligible at hadron colliders and thus not considered here. Before these mechanisms are discussed, the QCD factorisation theorem is introduced in the following.

Top Quark Production: The QCD Factorisation Theorem

Top quark pair production at high energies via proton-antiprotonp¯p(at the Tevatron) or proton- proton pp (at the LHC) collisions can be described by perturbative quantum chromodynamics (pQCD). Such hard scattering processes originate from the interactions between the constitutents of the two colliding hadrons, namely quarks and gluons, which are summarised by the term parton in the following. The subsequent paragraph describes the determination of the t¯t cross-section.

The probability density to observe a partonihaving a momentum fractionx_i at momentum transfer Q² within a hadron is mathematically expressed by parton distribution functions, abbreviated as PDFs, f_i(x_i,Q²) [60–62]. Such a ratio x of the parton momentum to the total momentum is often also referred to as Bjorken-x. Quark and gluon PDFs, however, cannot be directly predicted a-priori by means of QCD. So-called DGLAP equations[60–62], short for Dokshitzer-Gribov-Lipatov- Altarelli-Parisi, fulfil the purpose of describing the evolution of the PDFf_i(xi,Q²)for a fixed value of x_i. These PDFs serve to calculate the cross-section of top quark events, here shown as an example for t¯tpairs. In the next step, the cross-section of two incoming and colliding partonsiandj, denoted as ˆσ^{i j→t}^¯^t, is convolved with the PDFs f_i and f_j, evaluated at an energy scale, called factorisation scaleQ²=µ²_F. This scaleµF and the renormalisation scale, as introduced in Sec. 2.1.2, are set to a value that reflects the energy scale of the analysed process; in case of top quark events, the top quark mass is a common and reasonable choice: m_t=µF =µR. Therefore, one can derive the t¯t cross-section for proton-proton collisions at the LHC given the centre-of-mass energies of the pp collisionp

sand of the parton-parton collisionp ˆs[63]: σ^pp^→^t¯^t(p

s,m_t) = X

i,j=g,q,¯q

Z

dx_idx_jf_i(x_i,µ²_F)f_j(x_j,µ²_F)

·σˆ^{i j→t¯}^t(mt,p ˆ

s,x_i,x_j,αs(µ²_R),µ²_R).

A general expression of this term isQCD factorisation theoremas already indicated by the title of this paragraph. The name originates from thefactorisationof the production process (pp→t¯t here) into two components: The cross section of the hard interaction process (i j→t¯t) and the PDFs of the two participating partons in the initial stateiand j. It is the theoretical basis for cross-section calculations and cross-section measurements of top quarks as described in the next subsections.

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Top-Antitop Quark Pairs

Pairs of top-antitop quarks are produced via the strong interaction by two different processes, either q¯qannihilation with a quarkqand an antiquark ¯qorg g fusion. For the latter process, g g→ t¯t, three leading order (LO) Feynman diagrams exist whereas one Feynman diagram visualises the reactionq¯q→t¯t, as illustrated in Fig. 2.1.

Figure 2.1: Feynman diagrams for t¯t production via the strong interaction at lowest order.

Depicted are the diagrams of bothq¯qannihilation (top) and gluon fusion (bottom).

With a rising energy of the colliding particles, i.e. the centre-of-mass energy of the corresponding hadron collider, the cross-section of top quark production processes increases. This dependence of the cross-section for various important physics processes as a function of the centre-of-mass energy is visualised in Fig. 2.2. The cross-section for top quarks given in that figure contains not only t¯t production but also single top production. The curve indicates that the production cross-section at the design centre-of-mass energy of the LHC exceeds the value corresponding to the Tevatron collider significantly by around two orders of magnitude. This results in a huge amount of events involving top quarks which can be acquired by the LHC experiments. The cross-sections of other Standard Model processes increase with higher energies as well, though, these are considerably larger than the one of top quarks. Some of those events constitute important backgrounds of processes comprising top quarks, as described later in Sec. 2.2.2. The t¯tproduction also increases at the LHC, which is a ppaccelerator in contrast to the Tevatron that collidedpwith ¯p.

Theoretical calculations of the total production cross-sectionσ_t¯tof top quark pairs at the precision of full next-to-next-to-leading order (NNLO) which include soft gluon resummation at next-to-next-to- leading logarithmic (NNLL) order are available[64–68]. The latest calculations rely on a top quark mass ofm_t=172.5 GeV and the MSTW2008 68% CL NNLO PDF set[69, 70], using thetop++ 2.0 programme[71]for the evaluation. The following results are obtained for various centre-of-mass energies: The full NNLO calculation for t¯t production at the Tevatron atp

s=1.96 TeV assuming a top quark mass ofm_t=173.3 GeV is 7.16⁺₋^0.20_0.23 pb. The measured result for the LHC atp

s=8 TeV,

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2 . 2 T H E T O P Q U A R K

Figure 2.2:Cross-sections (left axis) as well as events per second (right axis) of different important physics processes inp¯pandppcollisions at the Tevatron and the LHC. The additional two vertical lines correspond to the Run II centre-of-mass energy at the Tevatron collider and to the design centre-of-mass energy ofp

s=14TeV at the LHC, respectively. The given curve for top quark production labelled asσt comprisest¯tas well as single top quark production. According to the colliding particles used at the Tevatron and the LHC, the cross-sections shown at lower energies refer top¯pcollisions while the ones at higher energies are based onppcollisions. The curve for top quark production reveals a step exactly at the transition between the two regions forp¯pandppcollisions atp

s=4TeV which arises because valence quarks instead of sea quarks - which are less likely to occur - contribute toq¯qannihilation inp¯pcollisions leading to the small

dip atp

s=4TeV when switching to appcollider [72].

Direct Top Quark Decay Width Measurement in the tt Lepton+Jets Channel at 8 TeV with the ATLAS Experiment

Direct Top Quark Decay Width Measurement in the t ¯ t Lepton + Jets Channel at p

s = 8 TeV with the ATLAS Experiment

Direct Top Quark Decay Width Measurement in the t ¯ t Lepton + Jets Channel at p

s = 8 TeV with the ATLAS Experiment

Abstract

Direkte Zerfallsbreitenmessung des Top-Quarks im t ¯ t -Lepton + Jets-Zerfallskanal bei p

s = 8 TeV mit dem ATLAS-Experiment

Zusammenfassung

Contents

1 Introduction

2 The Standard Model and the Role of the Top Quark Therein

2.1 The Standard Model of Particle Physics

2.2 The Top Quark